Naturally occurring copper is a mixture of two isotopes. One of these has 34 neutrons the other has 36. If the relative atomic mass of copper is 63.55 amu calculate the natural abundances (percentages ) of the two isotopes.
Let X = fraction Cu63
and 1-X = fraction Cu65
---------------------
X*63 + (1-X)*65 = 63.55
Solve for X and 1-X and convert each from fraction to percent.
34x +36-36x --63.55
235_
naturall occuring copper consist of two stable isotops 63/29 cu and 65/29.
To calculate the natural abundances of the two copper isotopes, we need to use the principle of average atomic mass and the given relative atomic mass of copper.
The relative atomic mass of copper is 63.55 amu, which represents the average mass of all the naturally occurring copper isotopes, taking into account their relative abundances.
Let's denote the abundance of the isotope with 34 neutrons as x and the abundance of the isotope with 36 neutrons as (1 - x). We can then set up the equation:
(34 * x) + (36 * (1 - x)) = 63.55
Simplifying the equation gives:
34x + 36 - 36x = 63.55
-2x = 63.55 - 36
-2x = 27.55
Dividing by -2 on both sides gives:
x = -27.55 / -2
x = 13.775
Therefore, the abundance of the isotope with 34 neutrons (x) is 13.775%.
To find the abundance of the other isotope (36 neutrons), we can subtract the abundance of the first isotope from 100%:
Percentage of the isotope with 36 neutrons = 100% - 13.775% = 86.225%
So, the natural abundances (percentages) of the two copper isotopes are approximately 13.775% and 86.225% respectively.